Plenary Speakers

Abstract: Since early 2000, many interesting nanomaterials have been discovered. For example, the negative-index metamaterial was successfully constructed in early 2000 and its potential applications in subwavelength imaging and invisibility cloaks have inspired many researchers in the study of metamaterials in recent years. Graphene, a 2-D nanomaterial, which was rediscovered in 2004. Due to its outstanding electrical, mechanical, magnetic, and thermal properties, graphene has gained significant interest among scientists in various areas. The 2010 Nobel Prize in Physics was awarded to two graphene experts (Geim and Novoselov). In this talk, I will talk about the development and analysis of some mathematical models for simulating wave propagation in these new nanomaterials. Focus will be on a carpet cloak model and a graphene model. Some interesting numerical simulations by the time-domain finite element method will be presented. The talk should be accessible to general audiences.

Short Biography: Jichun Li is Professor of Mathematics and Director for Center for Applied Mathematics and Statistics in U. of Nevada Las Vegas. His previous positions include Postdoc Fellow at University of Texas at Austin, and Associate Director of Institute for Pure and Applied Mathematics (IPAM) in U. of California at Los Angeles (UCLA). Research areas include analysis of  finite element methods, high-order finite difference methods, RBF meshless methods, and applications in image processing and electromagnetic wave propagation. He has published over 130 journal papers and 2 monographs (one on "Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials", Springer Series in Computational Mathematics, vol.43, Springer, 2013).

 Currently, he serves as Editor-in-Chief of "Results in Applied Mathematics" and Managing Editor of "Computers & Mathematics with Applications" (both published by Elsevier).  

Abstract: Motion by surface diffusion is a type of surface-area-diminishing motion such that the enclosed volume is preserved and is important is many physical applications, including solid state de-wetting. In this talk I will describe a relatively recent diffuse interface model for surface diffusion, wherein the sharp-interface surface description is replaced by a diffuse interface, or boundary layer, with respect to some order parameter. One of the nice features of the new doubly degenerate Cahn-Hilliard (DDCH) model is that it permits a hyperbolic tangent description of the diffuse interfaces, in an asymptotic sense, but, at the same time, supports a maximum principle, meaning that the order parameter stays between two predetermined values. Furthermore, numerics show that convergence to the sharp interface solutions for the DDCH model is faster than that of the standard regular Cahn-Hilliard (rCH) model. The down side is that the new DDCH model is singular and much more nonlinear than the rCH model, which makes numerical solution difficult, and it is still only first order accurate asymptotically. We will describe positivity-preserving numerical methods for the new model and review some existing numerics. We will also describe very recent results on the rigorous Gamma convergence of the underlying diffuse interface energy.

Short Biography: Steven Wise has been a professor of mathematics at the University of Tennessee, Knoxville, since 2007. Before that, he was a postdoc at UC, Irvine, in Orange County California, where he worked with John Lowengrub and Vittorio Cristini on complex fluids, crystal microstructure, and cancer progression. He got a BS degree in mathematics in 1996 from Clarion University and did graduate work in mathematics at Virginia Tech and Penn State after that. He received his PhD in 2003 from the University of Virginia, where he studied engineering physics with Dr. William C. Johnson. He primarily teaches courses in numerical analysis, and, with Abner Salgado, wrote a graduate-level textbook on the subject entitled ``Classical Numerical Analysis: A Comprehensive Course," published by Cambridge University Press this year (2023). He also teaches courses in analysis and PDE from time to time. Dr. Wise works in the intersection of numerical analysis, partial differential equations, and soft matter physics. He builds models to study heat, mass, and current flow and the formation of interfaces in complex fluids and materials, and he designs efficient numerical methods to get approximate solutions. He is the author of over 100 publications and was recognized by Web of Science as a highly cited researcher in 2020 and 2022. 

Abstract: In this presentation, I will discuss the construction and results of numerical simulations quantifying flows around several species of soft corals. In the first project, the flows near the tentacles of xeniid soft corals are quantified for the first time. Their active pulsations are thought to enhance their symbionts' photosynthetic rates by up to an order of magnitude. These polyps are approximately 1 cm in diameter and pulse at frequencies between approximately 0.5 and 1 Hz. As a result, the frequency-based Reynolds number calculated using the tentacle length and pulse frequency is on the order of 10 and rapidly decays as with distance from the polyp. This introduces the question of how these corals minimize the reversibility of the flow and bring in new volumes of fluid during each pulse. We estimate the Péclet number of the bulk flow generated by the coral as being on the order of 100–1000 whereas the flow between the bristles of the tentacles is on the order of 10. This illustrates the importance of advective transport in removing oxygen waste. In the second project, the flows through the elaborate branching structures of gorgonian colonies are considered.  As water moves through the elaborate branches, it is slowed, and recirculation zones can form downstream of the colony. At the smaller scale, individual polyps that emerge from the branches expand their tentacles, further slowing the flow. At the smallest scale, the tentacles are covered in tiny pinnules where exchange occurs. We quantified the gap to diameter ratios for various gorgonians at the scale of the branches, the polyp tentacles and the pinnules. We then used computational fluid dynamics to determine the flow patterns at all three levels of branching. We quantified the leakiness between the branches, tentacles and pinnules over the biologically relevant range of Reynolds numbers and gap-to-diameter ratios, and found that the branches and tentacles can act as either leaky rakes or solid plates depending upon these dimensionless parameters. The pinnules, in contrast, mostly impede the flow. Using an agent-based modeling framework, we quantified plankton capture as a function of the gap-to diameter ratio of the branches and the Reynolds number. We found that the capture rate depends critically on both morphology and Reynolds number.

Short Biography: Laura Miller is a Professor of Mathematics and Adjunct Professor in Biomedical Engineering at the University of Arizona. She received her Ph.D. from the Courant Institute of Mathematics at New York University where she worked with Charles Peskin to understand the aerodynamics of tiny insect flight. She then continued her work in biological fluid dynamics with Aaron Fogelson and Jim Keener at the University of Utah as a postdoctoral fellow. Using her training in both mathematics and biology, she continues to apply mathematical modeling and computational fluid dynamics to better understand how organisms interact with their environments and how organs drive flow in the body. Her current research interests include the feeding and swimming mechanics of jellyfish, blood flow in the embryonic heart, the consequences of flow around corals, and the aerodynamics of flight in the smallest insects and spiders.